Dear we can apply conservation of energy 1/2 m v^2 + 1/2 mR^2 ( omega ) ^2 + mgr + 1/2 m ( v - omega R )^2 = 1/2 m v' ^ 2 + 1/2 m R^2 ( omega ' ) ^2+ mgR + 1/2 m ( v' ^2 + omega R )^2 + mg2R
where v = velocity when the small mass is at lowest position v'= Velocoty when the small mass is at highest position omega = angular speed when the small is at the lowest position omega ' = angular speed when the small is at the highest postion
as the ring is rolling
v = omega R v' = omega ' R
Substituting
V ^ 2 = 3 v' ^2 + 2 g R
the catch of the question is The with the small mass is an inhomogeneous body The CG of the system is at a distance of R/2 Above the centre . It acceleration = omega' ^2 X R/2 ( down ward )
Moderation Team
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